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Notes section 4.7

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Notes for Section 4.7 - Geometry

Notes for Section 4.7 - Geometry

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    Notes section 4.7 Notes section 4.7 Presentation Transcript

    • Section 4.7 Use Isosceles and Equilateral Triangles
    • THEOREM 4.7: BASE ANGLES THEOREM If two sides of a triangle are congruent, then the angles opposite them are congruent. If AB  AC, then  B   C
    • THEOREM 4.8: CONVERSE OF BASE ANGLES THEOREM If two angles of a triangle are congruent, then the sides opposite them are congruent. If  B   C, then AB  AC .
    • Example 1 Find the unknown measure.
    • Example 2: Find the value of x .
    • Example 3: Find the values of x and y.
    • Example 4: Find the perimeter of the triangle.
    • Example 5: Garden You plant a garden in the shape of a triangle as shown in the figure. What is the perimeter
    • Find the measures of  R,  S, and  T.
    • Unit 5.1 - Notes midsegment _ – a segment that connects the midpoint of two sides of a triangle. So LM, MN, and LN are the midsegments of triangle ABC .
    • Midsegment Theorem :
      • The segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.
    • EX 1: If QR = 18, then JK is half of it which means JK = 9. If PK = 8, then KR = 8 since K is the midpoint of PR. Since PR = 16 all together, JL is half of PR since it is between the two midpoints so JL = 8. If KL = 6, then PQ is double KL so PQ = 12. KR = 8, LR = 9, QL = 9, PJ = 6, JQ = 6 Perimeter of  PQR = 18 + 12 + 16 = 46 Perimeter of  JKL = 6 + 8 + 9 = 23
    • EX 2 : Place each figure in a coordinate plane in a way that is convenient for finding side lengths. Assign coordinates to each vertex.
      • a square with sides of length m
      • b) an acute triangle with base length b